A Bi-Level Stochastic-Robust MILP Framework for Coordinated EV Charging/Discharging with Battery-Degradation and Piecewise-Linear Network Constraints in Distribution-Level Smart Grids

This work proposes a novel bi level mixed integer linear programming (MILP) framework that simultaneously addresses distribution system operator objectives and EV aggregator profit maximization under uncertainty, while fully capturing network and battery dynamics. In the upper level, the distribution operator minimizes expected energy procurement cost and peak demand penalties across a set of forecast scenarios (±20 % PV and load deviations), subject to linearized DistFlow constraints rendered tractable via on the fly piecewise linearization. In the lower level, each of five aggregators maximizes day ahead market arbitrage revenue minus linearized battery degradation costs, bidding aggregate EV charge/discharge power into hourly markets. We enforce non simultaneous charge/discharge, state of charge and power limits across 200 EVs over a 24 hour horizon. The bi level program is reformulated into a single MILP using Karush–Kuhn–Tucker conditions and solved efficiently via Benders decomposition. Simulations on the IEEE 33 bus test feeder demonstrate up to 20 % peak load reduction, 15 % energy cost savings, zero network violations under worst case uncertainty, and a 12 % increase in aggregator profit compared to benchmark scheduling. The proposed model advances the state of the art by integrating market participation, robust optimization, and explicit battery aging considerations in a scalable, network aware EV scheduling framework.